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\chapter{Controlling negative diffusion in the presence of risk behavior changes} % top level followed by section, subsection
\label{chapter:risk}

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In Chapter \ref{chapter:game}, we analyzed intervention strategies
assuming the behavior of each individual remains the same before and
after taking interventions, which is not an accurate assumption in
some real world scenarios. Previous studies have shown imperfect
interventions and risk behavior changes can lead to perverse
outcomes. Thus, in this chapter, we study how to control negative
diffusion with the presence of risk behavior changes.

From the results in Chapter \ref{chapter:game}, we can see that Nash
equilibrium may not exist even without risk behavior changes. Using
game theory in the presence of risk behavior changes is going to be
extremely difficult. In this chapter, we formulate a network-based
model and use random graph techniques to understand how risk behavior
change in conjunction with failure of prophylactic interventions can
lead to perverse outcomes where ``less (intervention) is more
(effective)''. Our model captures the distinction between one- and
two-sided risk behavior change. In one-sided situations
(e.g. influenza/H1N1) it is sufficient for either individual in an
interaction to exhibit risk behavior change whereas in two-sided
situations (e.g. AIDS/HIV) it is necessary for both individuals in the
interaction to exhibit risk behavior change, for a potential
transmission of the disease. A central discovery is that the
phenomenon of perversity occurs at differing levels of intervention
coverage depending upon the ``sidedness'' of the interaction.
Furthermore, again dependent on the ``sidedness,'' targeting highly
connected nodes can be strictly worse than uniformly random
interventions at the same level of coverage.

In Section \ref{sec:risk.models}, we formally define our model. In
Section \ref{sec:risk.results.sideness}, we explain our first finding
where less intervention can be more effective. In Section
\ref{sec:risk.results.target-random}, we explain our second finding
where targeted intervention strategy can be worse than random
intervention strategy. Section \ref{sec:risk.simulation} backs up our
findings with comprehensive simulations. And we conclude this Chapter
in Section \ref{sec:risk.conclusion}.

\input{5_risk/model}
\input{5_risk/results}
\input{5_risk/conclusion}

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